logo

Show the Proof

In [1]:
import proveit
# Automation is not needed when only showing a stored proof:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%show_proof
Out[1]:
 step typerequirementsstatement
0instantiation1, 2, 3  ⊢  
  : , : , :
1reference11  ⊢  
2instantiation4, 5  ⊢  
  : , : , :
3instantiation6, 7, 8, 9, 10*  ⊢  
  : , : , :
4axiom  ⊢  
 proveit.logic.equality.substitution
5instantiation11, 12, 13  ⊢  
  : , : , :
6theorem  ⊢  
 proveit.numbers.division.frac_cancel_left
7instantiation72, 15, 14  ⊢  
  : , : , :
8instantiation72, 15, 16  ⊢  
  : , : , :
9instantiation17, 18, 19  ⊢  
  : , : , :
10instantiation20, 26  ⊢  
  :
11axiom  ⊢  
 proveit.logic.equality.equals_transitivity
12instantiation21, 32, 33, 66, 34, 22, 36, 26, 37, 38  ⊢  
  : , : , : , : , : , : , :
13instantiation23, 33, 24, 32, 25, 34, 26, 36, 37, 38  ⊢  
  : , : , : , : , : , :
14instantiation72, 28, 27  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
16instantiation72, 28, 29  ⊢  
  : , : , :
17theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
18instantiation72, 73, 30  ⊢  
  : , : , :
19instantiation31, 32, 66, 33, 34, 35, 36, 37, 38  ⊢  
  : , : , : , : , : , :
20theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
21theorem  ⊢  
 proveit.numbers.multiplication.leftward_commutation
22instantiation45  ⊢  
  : , :
23theorem  ⊢  
 proveit.numbers.multiplication.association
24theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
25instantiation39  ⊢  
  : , : , :
26instantiation72, 73, 40  ⊢  
  : , : , :
27instantiation72, 42, 41  ⊢  
  : , : , :
28theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
29instantiation72, 42, 43  ⊢  
  : , : , :
30instantiation52, 44, 46  ⊢  
  : , :
31theorem  ⊢  
 proveit.numbers.multiplication.disassociation
32axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
33theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
34theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
35instantiation45  ⊢  
  : , :
36instantiation72, 73, 53  ⊢  
  : , : , :
37instantiation72, 73, 54  ⊢  
  : , : , :
38instantiation72, 73, 46  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
40instantiation72, 47, 48  ⊢  
  : , : , :
41instantiation72, 50, 49  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
43instantiation72, 50, 51  ⊢  
  : , : , :
44instantiation52, 53, 54  ⊢  
  : , :
45theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
46instantiation72, 61, 55  ⊢  
  : , : , :
47theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
48instantiation72, 56, 57  ⊢  
  : , : , :
49theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
50theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
51theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
52theorem  ⊢  
 proveit.numbers.multiplication.mult_real_closure_bin
53instantiation58, 59, 60  ⊢  
  : , : , :
54instantiation72, 61, 62  ⊢  
  : , : , :
55instantiation63, 64  ⊢  
  :
56theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
57instantiation72, 65, 66  ⊢  
  : , : , :
58theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
59instantiation67, 68  ⊢  
  : , :
60theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
61theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
62theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
63theorem  ⊢  
 proveit.numbers.absolute_value.abs_nonzero_closure
64instantiation69, 70, 71  ⊢  
  :
65theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
66theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
67theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
68theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
69theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
70instantiation72, 73, 74  ⊢  
  : , : , :
71assumption  ⊢  
72theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
73theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
74instantiation75, 76  ⊢  
  :
75theorem  ⊢  
 proveit.physics.quantum.QPE._delta_b_is_real
76theorem  ⊢  
 proveit.physics.quantum.QPE._best_round_is_int
*equality replacement requirements